Higher Check In -10.03Area calculations

  1. Calculate the total area of the shape below.
  1. Calculate the area of the sector, giving your answer in terms of .
  1. The area of the trapezium is 75cm2. Work out the length of x.
  1. A semicircle has an area of cm2. What is the length of its diameter?
  1. Calculate the area of this parallelogram.
  1. Ali says that the area of the triangle below can be worked out by calculating giving 40cm2. Petra says that the area is 20cm2. Show that Petra is correct.
  1. The diagram shows an equilateral triangle ABC with side length 12cm. P is the midpoint of AB and Q is the midpoint of AC. Show that the shaded area is 43.5cm2 to 3significant figures.
  1. Show that the total shaded area is 99.5cm2.
  1. The diagram represents a circular pond with a path that is 75cm wide around it. Mr Smith is going to cover the path in gravel. One bag of gravel covers 2m2. How many bags of gravel will Mr Smith need to buy?
  1. Calculate the area of a regular hexagon with sides of length 8cm.

Extension

A rectangular paddock is to be made using 120m of fencing.

Plot a graph with length (m) on the horizontal axis and area (m2) on the vertical axis.

What is the largest possible area for the paddock? Explain how you worked this out from your graph.What values of length and width give the largest possible area for the paddock?

Answers

  1. 420.5cm2
  1. cm2
  1. 7.25cm
  1. 2.5cm
  1. 82.7cm2
  1. 8cm is the slant height not the perpendicular height. The formula can only be used if you know the base and perpendicular height.

Using Area gives Areacm2, so Petra is correct.

  1. Shaded area area of triangle – area of sector

Shaded area, so 43.5cm2 to 3sf.

  1. Area of top left-hand grey trianglecm2.

Area of bottom right-hand grey trianglecm2.

Total area of central grey stripe cm2.

Therefore the area of the quadrilateral iscm2.

  1. The area of the path is given bym2, so he needs 3 bags of gravel.
  1. Divide the hexagon into 6 equilateral triangles.

Area of one trianglecm2

Total area cm2 (3sf)

Extension

Length (m) / 5 / 10 / 15 / 20 / 25 / 30 / 35 / 40 / 45 / 50 / 55
Width (m) / 55 / 50 / 45 / 40 / 35 / 30 / 25 / 20 / 15 / 10 / 5
Area (m2) / 275 / 500 / 675 / 800 / 875 / 900 / 875 / 800 / 675 / 500 / 275

The greatest area is 900m2 as the graph of area against length is a curve which has a maximum at (30, 900).

The greatest area is achieved when the length and width are both 30m, that is, when the paddock is square.

Assessment Objective / Qu. / Topic / R / A / G / Assessment Objective / Qu. / Topic / R / A / G
AO1 / 1 / Apply area formulae to find the area of a composite 2D shape / AO1 / 1 / Apply area formulae to find the area of a composite 2D shape
AO1 / 2 / Find the area of a sector / AO1 / 2 / Find the area of a sector
AO1 / 3 / Use the area formula for a trapezium / AO1 / 3 / Use the area formula for a trapezium
AO1 / 4 / Find the diameter of a semicircle given the area / AO1 / 4 / Find the diameter of a semicircle given the area
AO1 / 5 / Find the area of a parallelogram using the area sine rule / AO1 / 5 / Find the area of a parallelogram using the area sine rule
AO2 / 6 / Apply the sine rule to find the area of a triangle / AO2 / 6 / Apply the sine rule to find the area of a triangle
AO2 / 7 / Find a shaded area using area formulae / AO2 / 7 / Find a shaded area using area formulae
AO2 / 8 / Find the area of a composite shape using area formulae / AO2 / 8 / Find the area of a composite shape using area formulae
AO3 / 9 / Solve a real life problem involving area of a circle / AO3 / 9 / Solve a real life problem involving area of a circle
AO3 / 10 / Find the area of a regular polygon by splitting it into triangles / AO3 / 10 / Find the area of a regular polygon by splitting it into triangles
Assessment Objective / Qu. / Topic / R / A / G / Assessment Objective / Qu. / Topic / R / A / G
AO1 / 1 / Apply area formulae to find the area of a composite 2D shape / AO1 / 1 / Apply area formulae to find the area of a composite 2D shape
AO1 / 2 / Find the area of a sector / AO1 / 2 / Find the area of a sector
AO1 / 3 / Use the area formula for a trapezium / AO1 / 3 / Use the area formula for a trapezium
AO1 / 4 / Find the diameter of a semicircle given the area / AO1 / 4 / Find the diameter of a semicircle given the area
AO1 / 5 / Find the area of a parallelogram using the area sine rule / AO1 / 5 / Find the area of a parallelogram using the area sine rule
AO2 / 6 / Apply the sine rule to find the area of a triangle / AO2 / 6 / Apply the sine rule to find the area of a triangle
AO2 / 7 / Find a shaded area using area formulae / AO2 / 7 / Find a shaded area using area formulae
AO2 / 8 / Find the area of a composite shape using area formulae / AO2 / 8 / Find the area of a composite shape using area formulae
AO3 / 9 / Solve a real life problem involving area of a circle / AO3 / 9 / Solve a real life problem involving area of a circle
AO3 / 10 / Find the area of a regular polygon by splitting it into triangles / AO3 / 10 / Find the area of a regular polygon by splitting it into triangles